Computer



March 11, 1947. D. E. WILCOX COMPUTER Filed Sept. 5, 1945 2 Sheets-Sheetl INVENTOR. 00%: E. W/LCOX ATTORNEYJ' March 11, 1947. D. E. WILC OX2,417,098

COMPUTER Filed Sept. 5, 1945 2 Sheets-Sheet 2 m ENTOR. 00w: 5. W/LC 0XBY w 2* Arron/V675 atented Mar. 11, 1947 COMPUTER Doyle E. Wilcox,Pasadena, Calif., asslgnor to Consolidated Engineering Corporation,Pasadena, Calif., a corporation of California Application September 5,1945, Serial No. 614,550

Claims.

This invention relates to electrical addition systems and moreparticularly to systems for indicating voltage sums by the use ofelectrical impcdance elements. The principal object is to provide anelectrical system for indicating the equality of sums of voltageswithout errors.

In the copending applications of Clifiord E. Berry, Serial No. 561,192,filed October 31, 1944, and Serial No. 610,457, filed Aug. 13, 1945,executed August '7, 1945, assigned to the same assignee as the presentapplication, there is described an electrical addition system adapted toadd a plurality'of voltages and to indicate when the addition isproperly made. The said Berry addition system is shown as part of anelectrical computing system for solving simultaneous equations. Thequantities added in the equation are set up on suitable electricalnetworks for that purpose. and the electrical voltages representing thequantitles are then added by the addition system in accordance with theequation, a suitable indication being provided when the addition hasbeen made.

The electrical quantities to be added are taken as voltages across animpedance or potentiometer, which are individually applied to relativelyhigh impedances or resistances; and the resistances or high impedancesare together applied to a null indicator which indicates by its readingthe condition of equality of the voltage sums in accordance with theequation.

In that arrangement, the voltages for operating the computing system areprovided by a balanced source of A. C. voltage. Negative and positivesigns of the added quantities are provided for by applying the operatingvoltage to the corresponding network from one side or the other of thebalanced voltage supply source. In its operation there have sometimescrept into the results some slight errors arising from phase shift inthe power transformer and circuit with variations in the applied load atdifferent adjustments of the network elements.

According to my present invention, I provide a circuit arrangementmaking use of the fundamental addition circuit shown in the Berryapplications, but providing means whereby the voltages applied to thenull indicator correspond in phase as well as in amplitude, inconsequence of which variations due to circuit loading conditions do notaffect the null reading. More part cularly, I provide a balancedarrangement of the resistances or impedances of the addition system,with reference to the null indicator.

I make provision for the positive and negative signs in the equation bythe provision of switching means for switching the voltages representingthe quantities from one side to the other of the null indicator inaccordance with the mathematical signs. By this expedient those circuitelements whose output voltages are to be added may be connected inparallel, and changes in load on the power supply do not have the effectof disturbing the null indication.

As a refinement, I provide suitable shunting capacities across theresistors in the addition circuit for balancing the stray capacities.

The foregoing and other features will be better understood from thefollowing detailed description taken in conjunction with theaccompanying drawings of which:

Fig. 1 shows a system of the type disclosed in the Berry applicationSerial No. 561,192, in which voltages are added; and

Fig. 2 shows an electrical addition system in which voltages are addedaccording to my invention.

Fig. 1 shows an electrical computing system of the type shown in thesaid Berry application Serial No. 561,192 and is described briefly herefor the purpose of illustrating an application of my novel additionsystem. The system is adapted to solve for the three unknowns X1, X2 andX3 in the following simultaneous equations:

in which all of the quantities except X1, X2 and X3 are known. Theunknown quantity X1 is represented by the proportion of the voltageacross potentiometer 4 which exists between ground and the tap on thepotentiometer. The unknown quantity X2 is represented by the proportionof the voltage across potentiometer 5, which exists between ground andthe potentiometer tap. The unknown quantity X3 is represented by theproportion of the voltage across potentiometer 6 which exists betweenground and the potentiometer tap.

The set of potentiometers I, 8, 9 and III are for the known quantitiesof Equation 1, the quantity A11 being represented by the proportion ofthe voltage across potentiometer I between the tap and ground, and theother known quantities being similarly marked on their respectivepotentiometers. In similar fashion, the set of potentiometers ll, l2, l3and M represent the known quantities of Equation 2, and the set ofpotentiometers l5, I6, I! and I8 are for the known quantities inEquation 3 as marked on the potentiometers.

Four multiple switches, S1, S2, S3 and S4 are used, each having threecontact points I, 2 and 3. The switches are adapted to be thrown inunison by a single control member U so that all the switch points are oneither contact I, or 2, r 3. When the switches are thrown to theircontacts I, only Equation 1 is being computed,

and similarly when the switches are thrown to l point grounded; and thevoltage is taken from the transformer either between terminal 2| andground or between terminal 22 and ground. Potentiometers l, 8 and 9 areconnected in parallel across the lower half of coil 20, that is, betweenground and terminal 2|; while potentiometer I0 is connected across theupper half of coil 20, between ground and terminal 22. Thus the voltageimpressed on potentiometer I0 is 180 out of phase with the voltageimpressed on potentiometers l, 8 and 9; and this phase reversal takescare of the fact that M1, set up on potentiometer I0, is on the oppositeside of the equality sign from the other quantities set to providevoltages between ground and the respective taps which are proportionalto the numerical value intended to be set up. In other words, the tap isset so that the ratio of the voltage between ground and the tap to thetotal voltage across the potentiometer is equal to the known A or Mvalue. For this purpose it is convenient to consider the A and M valuesas decimal quantities which are fractions of unity; and if they are notalready fractional values the equations may all be multiplied through bya constant which will make them all fractions. Then the said voltageratios can be set to be equal numerically to the correspond- 1 ingfractions. If the voltage across all the A potentiometers (and the Mpotentiometers) be made 1 volt, for example, the fraction will benumerically equal to the voltage between ground and the tap of therespective potentiometer,

By reason of the connection of each tap through the respective one ofthe switches S1, S2, S3 and $1, the voltages representing the Acoefiicients are applied across the respective po tentiometers 4, 5 and6. proportion of the voltage between ground and the taps of these latterpotentiometers will represent the unknown quantities X1, X2 or X: bywhich the known coefficients are multiplied in the equation. Consideringnow the first of the equations,

it is only required that the unknown quantities X1, X2 and X2 bemutually adjusted so that the sum of voltages representing threequantities at the left of the equality sign be equal to the quantity atthe right of the equality sign. This is done by use of the additionsystem comprising the equal resistors R1, R2, R3 and R4. One side ofeach of these four resistors is connected to the respective taps 0f thepotentiometers 4, 5, 6 and Ill. The opposite sides of the four resistorsare connected together at the common terminal and to the null indicator22. Whenever the null indi- In consequence, the

4 cator indicates zero voltage, Equation 1 is satisfled.

Although there are shown in Fig, 1 three potentiometers 4, 5 and 6) forthe unknowns and four R resistors (R1, R2, R3 and R4) for performing theaddition, it will be recognized that there will be as many of the Xpotentiometers as there are unknowns. If there are n unknowns (andequations) there will be 11 unknown potentiometers and n+1 of the Rresistors.

The resistors R1, R2, R3 and R4 with their associated respective voltagesources, namely potentiometers 4, 5, 6 and I0 constitute an additionnetwork in which the resultant voltage across the parallel branches,that is across the null indicator I3 is given by the equation:

where,

E1 is the resultant voltage across the null indicator, and

e1 is the voltage between ground and the tap of ground and the tap ofthe nth potentiometer.

The summation is properly made according to the equation, when E1 iszero as indicated by a zero reading on the null indicator.

In order to have this summation equation hold accurately at difierentsettings of potentiometers 4, 5, 6 and ID the impedance of thesepotentiometers should be made negligibly small relative to the impedanceof R1, R2, R3 and R1. A convenient relationship is for R1 to R4 each tobe about one thousand times greater than the impedance of any ofpotentiometers 4, 5, 6 and I0.

Although the system of Fig. 1, as shown, is adapted to solve for theequation when all of the quantities of the equation are of a positivevalue, it can easily be adapted to take care of any negative quantitiessimply by connecting the ungrounded side of the A potentiometercorresponding to that negative quantity from the side of transformerwinding 20 on which it is now shown, to the other side. Thus, ifquantity A12, for example, is a negative number, the ungrounded side ofpotentiometer 9 instead of being connected to terminal 2| would beconnected to terminal 22. This would shift its phase by so that itcorresponds to a negative number, This same switching could be done withany of the known potentiometers and if desired, a suitable switch couldbe arranged for the purpose.

Such switching from one side to the other of the transformer secondaryintroduces irregularlties due to phase shift and other unbalances,however, which tend to impair the accuracy. Even without the switchingfrom the one side to the other of the balanced transformer, someirregularities are introduced by the changes in loading on thepotentiometer by changes in the taps on the potentiometers.

According to my invention, I avoid errors due to such irregularities bythe use of an addition system set up as shown in Fig. 2. In Fig. 2 thepotentiometers 4, 5, 6, 7, 8, 9 and I0 correspond to the same numberedpotentiometers in Fig. 1; the voltage source V corresponds to thevoltage source V in Fig. 1, and the transformer T corresponds to thepower transformer in Fig. 1. In Fig. 2, only those known potentiometers,1, 8, 9 and I for Equation 1 are shown, it being understood that thecorresponding known potentiometers for the other equations may bepresent and connected in circuit with their corresponding Xpotentiometers by their switches S1, S2, S3 and S4, as indicated.

The voltages to be added according to the summation called for byEquation 1 are the voltages at the taps of potentiometers 4, 5, 6 andI0, these being the same voltages as are added in Fig. 1. In Fig. 2, thesummation is made by use of resistors R1, R2, Ra and R4 the same as byuse of the same designated resistors in Fig. 1. This summation isapplied to the null indicator N, but in a somewhat difierent manner fromthe arrangement of Fig. 1. Instead of there being only one R resistorsuch as R1, R2, etc.,

' attached to each of the potentiometers 4, 5, etc.,

there are two of these R resistors. The potentiometer 4 for example, hasa resistor R1 connectable to its tap and another resistor R1 connectableto the grounded terminal. Likewise, the potentiometers 5, 6 and II! haveconnected to their grounded terminals resistors R2, R3, R1,respectively, these being each equal to R2, R3 and R4.

Accordingly, there is a, pair of the high resistors, that is, an R and Rresistor, for each X potentiometer, these being on each side of thetapped off portion of the voltage from the X potentiometer. These,instead of being attached directly to the null indicator N, are attachedon opposite sides of the primary winding Wp of transformer T11, thesecondary Ws of which is connected across the null indicator N.

It will be observed that the R and R resistors are not connecteddirectly to their corresponding unknown potentiometers, but through therespective reversing switches SR1, SR2, SR3 or $11,. Each of thereversing switches comprises two upper contacts a and b, respectivelyand two lower contacts c and d, respectively. When the reversingswitches are all thrown to their upper pair of contacts a, b, the Rresistor of the pair is connected to the upper side of the primary ofthe transformer Tn, and the R of the pair is connected to the lowerterminal of the transformer winding. When on the other hand, any of thereversing switches is thrown to its lower contact c, d, respectively,the polarity of the voltage from the respective unknown potentiometersis applied to the transformer T11 in the opposite polarity.

The summation called for by the equation is had when the two terminals30 and 3| of the primary T1) are at the same voltage, no current flowsthrough the transformer. This condition will be indicated by a nullreading on null indicator N connected across the secondary Ts. Underthis condition, the sum of the voltages brought to terminal 30 byresistors R1, R2, R3 and R4 is equal to the sum of the voltages broughtto terminal 3| by resistors R1, R2, R3 and R4.

It will be noted that the connections are arranged to provide thesummation called for by Equation 1. Thus, all three of the unknownquantities X1, X2 and X3 are at +he left of the equality sign, and withthe SR, reversing switches all in their upper positions, as shown, theresistors R1, R2 and R3, from the taps of the unknown potentiometers 4,5 and 5 are brought to terminal 30. The tap for quantity M1 set up onpotentiometer Ill however, is brought to resistor R1, which goes to theother terminal 3| of the transformer. This is in accord with theequation wherein the M1 quantity is at the righthand side of theequality sign. Thus, the connections are proper to equate the sum of thequantities at the left of the equality sign to the quantity at the rightof the equality sign.

In an analogous manner, the resistors R1, R2 and R3 from the ground sideof the unknown potentiometers are all brought to terminal 3| of thetransformer, while resistor R1 from the ground side, of the M1potentiometer is brought to the opposite terminal 30, thus establishingthe equality called for by the equation for the ground side of thesystem.

If any of the quantities in the equation is a negative value instead ofthe positive values shown in the equation, this negative sign is easilytaken care of by reversing the corresponding S11 switch. Thus, if thecoeflicient of X: be a negative number, the switch S11 connected withpotentiometer G is thrown to the down position, thereby reversing thepolarity of the voltages put on the respective resistors R3 and R3.

Further refinements of my system are the provision of trimmer condensersfor balancing the capacities across the resistors and to ground. Atrimmer condenser C1 is connected from terminal 30 to ground, and asimilar trimmer condenser C1 is connected from terminal 3| to ground;these may be adjusted to balance the two sides of the primary Tp withreference to ground.

Similarly, a trimmer condenser Cr is connected acros each of theresistors R1, R2, Ra, R4 and Adjustment of these trimmer condensersenables the capacity across each of the resistors to be made the same.

The A values can be set up on the respective A potentiometers in anyconvenient manner. For example, if the voltage of source V be fixed atone volt, and if a voltmeter -be connected between ground and each Apotentiometer tap, the tap is set so that the proportion of the voltageacross the entire potentiometer which lies between ground and the tap isequal to the numerical value of the A in the equation, and thisnumerical value will be read directly on the meter. For example, if thevalue of A11 be .6291, and if the voltage across potentiometer I be onevolt, the tap of the potentiometer should be moved so that thevoltage-between ground and the tap appears on the meter as .6291 volt.

A more convenient and more accurate way of setting up the 1A quantities,however, is the arrangement shown in Fig, 2 to the right of the brokenline ZZ. This Wheatstone bridge arrangement comprises a potentiometer 40having the two bridge arms 40a and 40b separated by the tap 4| of thepotentiometer. A null indicator N2 is connected to this potentiometertap and the other side of the null indicator is connected to aselectorswitch 42 adapted to connect with any one of a series of taps 43. Eachof the selector switch taps connects to an individual one of the taps ofpotentiometers I to II]. Thus, the other two arms of the Wheatstonebridge are composed of the portions on either side of the potentiometertap of whichever of potentiometers I to It] is in circuit. The tap 4| onpotentiometer 40 is moved to tap off between ground and tap 4| theamount of the voltage bearing the ratio to the total voltage across thepotentiometer 40 which is equal to the particular A number to be set up.If this A number is being set up for example on potentiometer I, theselector switch is turned to its uppermost switch point 43, and then thetap of potentiometer I is moved until a null reading is had on nullindicator N2. This null reading indicates that the voltage on the tap ofpotentiometer 1 is the same as that on the tap of potentiometer 40, andtherefore isthe required A value. This same procedure can be followed toset the taps on each of the other potentiometers 8, 9 and I 0. Aspotentiometer 40 is not loaded, its increments of resistance aredirectly proportional to its increments of voltage. Accordingly, a scalemay be placed on potentiometer 40 to read directly the ratio of thevoltage on the tap to the total voltage across the potentiometer, andthus read directly the numbers to be set up. 1.

of the computer in solving these equations. The

first column gives the number of the cycle of operation, one cycle beingdefined as the process of solving'each of the equations once in themanner previously indicated. The second column gives the number of theequation being solved, and the next four columns show the values of theA and M coefilcients corresponding to the particular equation. The lastthree columns give the X approximations existing at that particularpoint in the operation, and the X which is solved for is underlined. Itshould be noted that in this example, the solutions were initiated byarbitrarily setting the X2 and X3 potentiometers at zero and thensolving for X1;

A eoefilcients X approximations Cycleof Equation be- M operation 111gsolved A111 A113 A113 X1 X: X:

(7) 1.0000 0.0105 0.0043 0.0301 0.0301 0 1w (s) 0 1.0000 .0470 .4131T0301 .4131 0 (0) 1.0000 .0341 .1512 .3505 .0301 74131 .4000 (7) 1.0000.0105 .0043 .0301 .0200 .4131 4000 (3 0 1.0000 .0470 .4101 71205 .30304000 (0 1.0000 .0341 .1512 .3505 .0200 F030 .5504 (7) 1.0000 .0195 .0043.0301 112.10 .3030 '50l (s) 0 1.0000 .0470 .4131 .0260 .3010 =5504 (0)1.0000 .0341 .1512 .3505 .0200 3010 5300 (7) 1.0000 .0105 .0043 .03010290 .3010 51100 (3 0 1.0000 .0470 .4131 .0200 3 000 5000 (0 1.0000.0341 .1512 .3505 .0200 .3000 009 As .the X potentiometers are notappreciably loaded (since resistors R1, R2, R1, R2, etc. are relativelyhigh) the increments of impedance on these potentiometers aresubstantially proportional to the increments of voltage. Accordingly, ascale can be fixed to each of these potentiometers on which the positionof the tap will read directly the ratio which the voltage from ground tothe tap bears to the total voltage across the potentiometer. The X valueset up can accordingly be read directly on the scale.

A numerical example showing the way in which solutions for simultaneousequations may be made on the computing system is given as followswherein Equations 4, 5 and 6 are the same as the Equations 1, 2, and 3,respectively, but with specific numbers for the known Values. In makingthis solution, it is assumed that the system of Fig. 2 I is being usedand that selector switches S1, S2, S3, S4 have connected to their taps 2and 3, the corresponding A potentiometers shown connected to these tapsin Fig. 1. The subscript n stands for the equation being considered.Thus when considering the first equation A111 is A11, A112 is A12 andA113 is A13; and when considering the second equation, A111 is A21, A112is A22, etc.

Let the set of equations to be solved be:

2.0000X1+.0390X2+.0086Xz=.0602 0X1+3.0000X2+.1428Xa=1.25431.0000X1+.6341X2+.1512Xs=.3565

1.0000X1+.0195X2+.0043X3=.0301 0X1+1.0000X2+.0476X3=.41811.0000X1+.6341X2+.1512X3=.3565

The following table summarizes the operation In this particular problem,four cycles of operation were required to reach the final answers whichare:

X1=.0200 X2=.3900 X3=.5900

In the foregoingproblem, the A and M values set up on the computer arevoltage ratios; that is, the coeflicient 1.0000 for the A111 value inEquation 7 means that the tap of potentiometer 1 is set at the top ofits potentiometer, so as to tap oil the entire voltage across thepotentiometer, the .0195 value for Aug means that the tap ofpotentiometer 8 is set at .0195 of the total voltage acrosspotentiometer 8, etc., etc. The final solution, .0200 for X1 was foundby ascertaining that after the final cycle of operation, the tap ofpotentiometer 4 was set on the potentiometer to tap off .0200.of thetotal voltage across the potentiometer, etc., etc.

The total impedances of the potentiometers and resistances are notcritical. It has been found that the following set of values canconveniently be used and preferably they are made to be as close aspossible to a pure resistance:

Potentiometer and impedance No. Value of impedance Potentiometers 4, 5,6 gotenttiometgs 7, 8, 9, l0

1,000 ohms, each. L000 ohms, each. 500.000 ohms, each. 1,000 ohms.

1. An electrical summation network, comprising a plurality of voltagesources, a null voltage indicating means and a pair of impedanceelements connected from each source to the indicating means, one of eachpair being connected from one side of its associated source to one sideof the indicating means, and the other of each pair being connected fromthe other side of its associated source to the other side of theindicating means, the impedances of said impedance elements being ofequal magnitude.

2. A network according to claim 1, in which the magnitude of theimpedance of each impedance element is high in comparison with theimpedance of the sources.

3. An electrical summation network comprising a plurality of voltagesources having a pair of output terminals, one of the output terminalsof each source being connected together at a common junction, a nullvoltage indicating means, and a pair of impedance elements connectedfrom each source to the indicating means, one of each pair beingconnected from the common junction to one side of the indicating means,and the other of each pair being connected from the other terminal ofthe associated source to the other side of the indicating means, theimpedances of said impedance elements being of equal magnitude.

4. An electrical summation network comprising a plurality of voltagesources, a null voltage indicating means, a pair of impedance elementsconnected from each source to the indicating means, one of each pairbeing connectable from one side of its associated source to one side ofthe indicating means, and the other of each pair being connected fromthe other side of the associated source to the other side of theindicating means, said impedances being of equal magnitude, and areversing switch in series with each of the impedance elements forreversing the polarity of each of the elements with respect to itsassociated source.

5. An electrical summation network comprising a plurality of voltagesources, a null voltage indicating means comprising a transformer.having a primary and a secondary winding and a null indicator incircuit with the secondary winding, and a pair of impedance elementsconnected from each source to the primary winding, one of each pairbeing connected from one side of its associated source, to one side ofthe primary winding, and the other of each pair being connected from theother side of its associated source'to the other side of the primarywinding, the impedances of said impedance elements being of equalmagnitude.

6. An electrical summation network comprising a plurality of voltagesources, a null voltage indicating means comprising a transformer havinginput terminals and output terminals and a null indicator connected incircuit with the output terminals, a pair of impedance elementsconnected from each source to the input terminals, one of each pairbeing connected from one side of its associated source to one of theinput terminals, and the other of each pair being connected from theother side of its associated source to the other of the input terminals,the impedances of the impedance elements being of equal magnitude, and atrimmer condenser connected from each of the input terminals of thetransformer to the common terminal.

7. An electrical summation network comprising a plurality of voltagesources, a null voltage indicating means, a pair of impedance elementsconnected from each source to the indicating means, one of each pairbeing connected from one side of its associated source to one side ofthe indicating means, and the other of each pair being connected fromthe other side of its associated source to the other side of theindicating means, the impedances of said impedance elements being ofequal magnitude, and a trimmer condenser connected across each impedanceelement.

8. An electrical summation network comprising a plurality ofpotentiometers arranged in parallel circuits with respect to each other,means for impressing an alternating voltage on the potentiometers andmeans for taking an output voltage from each of the potentiometers, oneof the output terminals of each potentiometer being joined at a commonterminal, and a pair of impedance elements connected from eachpotentiometer to the indicating means, one of each pair bei'ng connectedfrom the common terminal to one side of the indicating means, and theother of each pair being connected from the remaining output terminal ofits associated potentiometer to the other side of the indicating means,said impedance elements being of equal magnitude which is high relativeto the impedance of the potentiometers.

9. An electrical summation network comprising a plurality of voltagesources, a null voltage indicating means and a pair of impedanceelements connectable from each source to the indicating means, one ofeach pair being connectable from one side of its associated source toone side of the indicating means and the other of each pair beingconnectable from the other side of its associated source to the otherside of the indicating means, the impedances of said impedance elementsbeing of equal magnitude, and a double-pole, doublethrow reversingswitch in series with each pair of impedance elements to reverse theirpolarity with respect to the indicating means.

10. An electrical summation network comprising a plurality ofpotentiometers arranged in parallel circuits with respect to each other,means for impressing an alternating voltage on the potentiometer-s andmeans for taking an output voltage from each of the potentiometers, oneof the output terminals of each potentiometer being joined at a commonterminal and a pair of impedance elements connectable from eachpotentiometer to the indicating means, one of each pair beingconnectable from the common terminal to one side of the indicating meansand the other of each pair being connectable from the remaining outputterminal of its associated potentiometer to the other side of theindicating means, said impedance elements being of equal magnitude whichis high relative to the impedance of the potentiometers, and a reversingswitch in circuit with each pair of impedance elements to reverse itspolarity with respect to the indicator.

DOYLE E. WILCOX.

